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Relaxation Under Geometric Constraints I: Classical Processes

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An Introduction to Anomalous Diffusion and Relaxation

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Abstract

In this and the next chapter, we shall examine the relaxation behavior of classical and quantum systems under geometric constraints represented by structures known as comb models. These models with fractional time derivatives are a reasonable abstraction for systems in which the interplay between temporal and spatial disorders is present. The results provide theoretical knowledge about the importance of interaction between geometrical restrictions and memory effects on anomalous diffusion. This chapter focuses the anomalous diffusion process emerging in classical systems, also taking into account the presence of reaction-diffusion processes at the interfaces. A generalization of the comb model is analyzed as a tool to account for annealed and quenched disorder. The crossover between different diffusive regimes and its physical explanations point towards possible applications to some experimental contexts involving anisotropic diffusion and biophysical systems.

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Authors and Affiliations

  1. Departamento de Física, Universidade Estadual de Maringá, Maringá, Paraná, Brazil

    Luiz Roberto Evangelista

  2. Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, Paraná, Brazil

    Ervin Kaminski Lenzi

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  1. Luiz Roberto Evangelista
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  2. Ervin Kaminski Lenzi
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Correspondence to Luiz Roberto Evangelista .

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Evangelista, L.R., Lenzi, E.K. (2023). Relaxation Under Geometric Constraints I: Classical Processes. In: An Introduction to Anomalous Diffusion and Relaxation. PoliTO Springer Series. Springer, Cham. https://doi.org/10.1007/978-3-031-18150-4_8

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